Let α ₁, α ₂ are two values of α for which system 2 α x + y = 5, x - 6y = α and

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3 and 4 .Determinants and Matrices

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Let $ \alpha _1, \alpha _2$ are two values of $\alpha $ for which the system $2 \alpha x + y = 5, x - 6y = \alpha $ and $x + y = 2$ is consistent, then $ |2(\alpha _1 + \alpha _2)| $ is -

A

$21$

B

$23$

C

$25$

D

$27$

Solution

$\left|\begin{array}{ccc}{2 \alpha} & {1} & {5} \\ {1} & {-6} & {\alpha} \\ {1} & {1} & {2}\end{array}\right|=0$

$2 \alpha(-12-\alpha)-(2-\alpha)+5(7)=0$

$2 \alpha^{2}-24 \alpha-2+\alpha+35=0$

$2 \alpha^{2}-23 \alpha+33=0$

$\alpha_{1}+\alpha_{2}=\frac{23}{2}$

Standard 12

Mathematics

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